In logic, extensional and intensional definitions are two key ways in which the objects, concepts, or referents a term refers to can be defined. They...

classified into two large categories: intensional definitions (which try to give the sense of a term), and extensional definitions (which try to list the objects...

distinction between intensional and extensional entities is parallel to the distinction between sense and reference. Logic is the study of proof and deduction as...

According to an extensional definition, they are abstract groups, sets, or collections of objects. According to an intensional definition, they are abstract...

language is intensional if it contains intensional statements, and extensional otherwise. All natural languages are intensional. The only extensional languages...

the concept of intensionality, which is concerned with whether the internal definitions of objects are the same. The extensional definition of function equality...

mathematical logic: see intensional statement. See also extensionality, and also intensional definition versus extensional definition Intensional logic embraces...

free dictionary. Comprehension Enumerative definition Exemplification Extensional and intensional definitions Intension Ostension Wittgenstein, Ludwig....

of the original sentence. De dicto and de re Extension (semantics) Extensional definition Extensionalism Intensional logic Opaque context Propositional...

versions of the type theory: Martin-Löf proposed both intensional and extensional variants of the theory and early impredicative versions, shown to be inconsistent...

who has been tortured and left brain-damaged disjointedly repeats lines from the poem. Extensional and intensional definitions Plato's beard The Man Who...

Mearns poem Empty name Extensional and intensional definitions – Classification of definitions in mathematics, philosophy, and logic Meinong's jungle –...

phenomenology Experience Experience machine Explanation Extensional and intensional definitions Fact Fairness False Felicific calculus Fidelity Final anthropic...

An enumerative definition of a concept or term is a special type of extensional definition that gives an explicit and exhaustive listing of all the objects...

similarly to a set defined by its members. The class is extensional. A set defined intensionally is a set of things that meet some requirement to be a member...

implements function equality as extensional equality. Intensional equality Under intensional equality, two functions f and g are considered equal if they...

usage to see 'intension' used for both the composite and the primitive ideas. Extension Extensional definition Intension Intensional definition v t e...

Philosophical term denoting a group of things derived from extensional or intensional definition Formalism (philosophy) – Concept of focusing on form over...

'Axiom of Extensionality' has its roots in logic. An intensional definition describes the necessary and sufficient conditions for a term to apply to an object...

2, November 1978 "The Role of Intensional and Extensional Interpretation in Semantic Representations". Kent in "Data and Reality" : "One thing we ought...

identity and equivalence must be maintained, often with an interpretation of intensional equality (the equality on the original set) and extensional equality...

Frege's and Tarski's ideas. To overcome problems associated with extensional definitions of meaning, Carnap pioneered the study of intensional semantics...

whether the type theory is intensional or extensional. In 1934, Haskell Curry noticed that the types used in typed lambda calculus, and in its combinatory logic...

as Other Minds Double entendre Extension Extensional definition Intension Intensional definition Loaded language Metacommunicative competence Pun Semantic...

finality) corresponds directly to the appropriate induction principle. In intensional type theories with the univalence axiom, this correspondence holds up...

functional extensionality, UIP and K in fact sufficient to capture the differences between intensional and extensional Martin-Löf type theory: extensional MLTT...

extensional, while contexts in which extension is not enough are intensional. Mathematics is typically extensional throughout." Stanford University primer...

2013-03-12. Retrieved 2023-09-13. Hofmann, Martin (1997). "Extensional Constructs in Intensional Type Theory". SpringerLink. doi:10.1007/978-1-4471-0963-1...

Talcott, Carolyn (1985). The Essence of Rum: A theory of the intensional and extensional aspects of Lisp-type computation (Ph.D. thesis). Stanford University...

this assignment is only truly functorial in extensional type theories (see #Properties). In intensional type theories, such functions are not truly functors...